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Slalislical Analysis of Competition Soaring
ChristofMaul'Iechnische Unbersitiit Braun$hwei|, 38I06 Br.tu s.hweiS' Gemunv
Joha n Walfsang Coethe'Uniwtsildt, 604i37 FrunkI tt, Gennanvc.mrul @tu-braunschweig de
AbstractFlight log dala of three compelition days of the Liissc National Gl;ding Competition (Lilienthal
Glide 2007) have been rnalyzed to extritcl vertical spccd disrributio's and altitude dist.ib tions in
space and 1imc. Results are useful tbr forccaslers and t$k-selters likewisc Analvzed dalcs were
luly 16. July 23, and July 26. These datcs were chosen bccause lhev wcrc chrracteriTed bv a
homogenous wenther siturlion thoughout the day. so that tempoml evolution and spaLial
characteristics rellecl piloL slrntegies rathcr than weatbcr changes
Nomenclatureh altitudct rime (UTC)
y latjtudcw vefiicxl spced
v horlzontrl(air)speedflh) aliitudedistribuiionti.) vertical spccd dislijbutiorhj,, meanthennxlcnterirgrltitudeh"* nrean th€rmnl exiiing altiLude
h,,,"- maximumrltilude{,,(h) thermalenLcnngaltitudcdistributioni,,(h) thermal exiting altitude dislribution
lntrodoctionEstablishing lhe use ol srtellite nrvigadon-based llighl
dntn logge$ bas not only rcvolutioniTed soaring navignlion
rnd docum€nLrlion, blt xl$ provides acccss 1() x hugc scl ofdala which crn be employcd in ordcr lo charxctcrizemcicorologicrl condllions ortilois' tactical dccisionmaking
The shlistical analysis ol individual ll;ghls is a strDdard
dc bnefing proccdure fo. rtralyzing a pilor's pefbrmancc
Syslemalic srati(icrl aoalyscs of ensembles ol glider llightsarc lcss conrmonly tbund. notwirhstanding prcvious usc olin(rumenled b;ds lbr the invcsligaiion oi the convectivc
bountJary layerr''?. Previous work making usc of a staristical
npproactr iniluacs ttre ve.iticrtion of thermal torecastsr as wcllas scveral altenrpls to establish so called hot spot" darabrscs'n,l rhrL,l .rrrr.:lh Jnrl) r. '. lloue\e, ,Jur ro rverr6irrgover sc!eral days xnd large arcxs, lhe lattcr investigarions
nright lail 10 recognizc relevanl firLu rcs.
Thc nrotivalion for the work pr€serted hcrc was toinvcstigale thc rcal behavior of colnpelition pilois who
oplimize speed or llight disrancc under givcn condilions, as
comparcd to the rrther simplistic assumpLions underlying
speed to lly theoryr. Main issucs kr be considctcd are 1) the
disiibulion t1h) of flighr altitudes h and 2) the distdbution tlw)of ycrtical speeds w. As a nnllcr of tact. spccd loJly lh€o'ldocs not make assuftplions wilh rcspect to the altitude brndwhich is used by a pilol tbr cross count.y flighl othe. lhan
finding a liti bclire hilling tbc ground. Howcler. werthcrcondi(ions. in thc iast place thc w;nd veclor, rc not the same
.IF'IINICAI. SOARING 9'I
for all altiludes. Therelorc, the fligb! alLitudc will have rnimpact on thc pilot's pefbrmancc. even iflhc possible event ofan outlanding is not consideted. Secondly, spccd 1o-fly theory
assunes a fixed average climb rate value as crilerion fbraccepting r lift. Clearly, acLual as well as lifL averaged climbrxtes used by a cross country pilol will considetxbly vary in thc
conrse ofallighL.
NlcthodsIo order Lo wrrrant identical conditio.s iit thc data to be
xnalyzed. uight logs of llre Lil;cnthai Glide 2007 were chosen
lor raw data. Thc compedtbn wrs held in Liissc near Berlin,Germany, fro July 14 to 27, 2007, ir thrce classes (15n,I 8m. and OpcI)) witlr allogc$cr 97 competilrs All days wcrc
chxracteriz€d by no to fiw outlindings and a high linishingrxte. In t{rhl, 254 complctcd compeiilion llighls were
considered in Lhc.tnalysis (fordeLrils reler to Trblc l).First. flight logs \rere cleancd f.om prc start and post
linish datr poinls- Then. in order to reducc lhe number olpoinls without losing relevant information, Lhc mininum tinlcinlerval betwccn ndiacent data foints was scl 10 2'1 seconds.'fhis resulted in x sel of allogcthcr 126.904 data Points (cl.'t{blc l), each ol which is a vcclor consisiing ol livecomponents: timc t, lntilude y, bngilude x. ahitudc h, and
lcrtical speed w. For the calculrtion of vertical spccds w the
brometric altiludc inibrmat;on was used inslead oiGPs'basedaltilode readings bccause GPS bascd dala contain numerous
bad dntn points which would strongly afieci clnnb xnd sinkmLcs calculated tiom the r. For oblai.ing a reason$ly smooth
rcsult for the verdcal speed distribulion (w). it was ncccssary
to avcrage ove. two ncighboring I)oinls.Figure 1 shows thc accumulatcd flight lracks y(x) tur all
thrcc conpetilion drys. The area shown is 11.8"E o 15 0"Eand 5l.l'N to 52.3'N. Lrisse a'rlicld is rarked bv an open
c;rclc ncar lhe upper lcft corner ofcrch diagram. For aU three
drys, hsks ior all chsses covered r rclatively small drca (130
Lrl r-) 220 lrn, $hicI rcache. rlr. Pori h ,e,ri,. \ .n i.\eastern cdge and which is limited by the air spacc C olmetropolihn Berlin in the No{h and by the line Drcsdcn
Leipzig l-Irlle-Magdcburg in the South and in the Wcst
Figurc I shows that thc lask arca is dcnscly and .claLilclyhomogeneously trobed by the &cumulated iliSht Lracks Due
ro thc snall siTc and the honmgcnous chamctcr ol the
\ot. 32, NO. J Jtty scta. tbtt 2008
compelition area, no attempl has bccn mxdc 1(r analyze thespatial va.iation ofrhe flighl log data.
Figure 2 shows accumulated vadognms w(1) for aU threecompetition days. llxccpt for thc srart nnd nnal glide phase,
variation oI vcdical spccds is srnnll throughout the race. Thevertical speeds w shown hcre musl not be confused with themereorological movement oi thc air duc to sink rate and sticklift efiects.
First, vertical speeds w describe the aclurl lerticrlmovement oftlrc glider, not the updmit or downdraft ofthe airit flies in. Thus, the calcolated vcrdcal spccds w nre lowerthan the meteorological vrlues by the sink rate of the circlingglider. In padicular, the climb rales will bc smnller than theupdraft by the rate ofleast sink ofthe glide., rnd thc calculatedsink rates will refleci the (hodzontal) ai. speed v of the glidcrralher than any vertical speed of the air itself (providcd pilolsprcfcr 1() minimize the time they spend in sinking air). Sccond,vcnical spccds w are not coffected lbr changes in horizonLal
speed v, i.c. values in Fig.2 (and in the analysis ofthe VenicalSpeed scclion) contain rhe full eftbct of stick lift. Largeve.rical spcds w (posilive and negaiive) are almost ceftainlydue Lo this cllect ltnd should not be given loo much weight inthe iurLhcr anrlysis. Generally, the spread in vertical speeds wis slightlt cxaggcralcd lowrrds positive as well as towardsnegative valucs. Ncvcrthclcss, the number of such adificialdata points is small. Consider, fbr example, a typical changein horizonlal speed upon enlering a thermal tiom vr = 50 m/sto v, = 30 ds. The coresponding aldtudc gain isapproximately 80 n\ neglecting the effect of friclion. If thisrhLudc sain occurs within a single time interval of 24 s, thccorrcsponding data point ibr the vedcal speed w will bcshifted up by :1.4 n/s whereas all lbllowing data points for Lhc
sxmc thermal remain unaffeded. If the altiludc saincd in a
ther ral by circling is assumed to be 600 m at xn avcrage clinbrate of 2.5 nvs, there will be l0 data poinls sbowing correcivertical speeds lor one data poinl atfectcd by stick lift.
A conection of the data set for these two ciiccts was nol
fcrlormcd due lo the heterogeneity of the data that halc bccnobtained tiom 97 individual combinations ol glidcrs and flighirecorders. While glider polars arc normally available,information on weight and ballasl is nonnnlly missing. so theglider sink rale could be, at bcsl, csLjmrLcd roughly. Moreinportant, the elimination of both cllecLs would rcquire thedetermination of horizonLal ri. spccd ltnd its changes, whereasilight recordeN sarnple Sround spccd datx. Conversion of oneinto the other would require wind drtii whicb xrc not readilyivailable. Addjtionally. Lhe detcrminxtion ol changes inhorizontal speed requ;re a high samplnrg ralc ol the llightrecorder in order ro trecisely nrcnitor dircction changes made') rhc I il. r. rl f:rrrLl.r {l'il( cirJlinS. Ho$e\er. rninlnLrn
sampling rates in gliding compelitions are too small to allowlbr a clear seprraLnm bctwcen speed and direction change!.The extraction ol nrctcotulogicrl upd.aft fiol]l llight reco.derda1a. therefo.e, wonld bc tuasiblc only in a well'controlled
lrisure 3 sho$,s rccunNlaled barograms h(t) for rll tbrcccompclilion days. Variatior of allitude bands with tirDc ismo.c pronounced than the variation ol vcrticrl spccds.
VOl,. 12, NO.3 .tu|," Septenbet2A0E
Maximun altitudes and thcir varialion with time are indicatedin Fjg. 3 by horizontal solid lincs wilh 30 minu.e timeresolution. Stad and final glidc phases have not been
considered. July 16 is characlenzed by high llight aldtudesclose to the German lcgal nltitude limit of FL100. Therefore,lhe July 16 rllitudes relleci a legal barier ratber than a
meteorologjcal one and havc consequently not been used forlhe altitude aralysis.
Determining meteorologically mcaningfirl maxinlulnaltitudes js not a st.aightforwird lxsk- The largesi alritude in agiven 30 minute intcrvnl o' during a compelitior day is
certainly no! an appropriate valuc, in partjcular if a possibleallitude gain in the ord€r ol80 m by thc variation ofhodzontalspeed is considered. Therefore, Lhe somcwhat arbilrary valueoflhc 99.757, percentile has been chosen as maxinurn altjtudevalue h.*. This means that 99.75% ol all dala points have an
ltllitude snuller than h.*. This value correslonds nosl closelyLo whrl one would determine as the maximum allitudeirLuilively, but at the same time allows thc unbiased
Vertical spccdTwo kinds of vertical speed disLributions f(w) are
presented. The firsi has rcsultcd irom integrating over tullcompetiijon days. The second onc has bccn obtained with a 30minute tinre rcsolulion and allows onc to follow the evolulionofthermals and the flyirg stratcgy dudng lhe flight.
Time-integruted vertical speed disiributionsTime'inregrared lertical spccd dislributions f1w) fbr each
of the lhree days under consideraLion rrc shown in Fjg. 4.Basically, they have been obtaincd by projecting theaccumulated variograms w(t) in l-ig.2 onlo the w axis.
Qualitrlively, thc distributions lbr all three days are identical-All are charrctcrizcd bl a bnnodal disaibution, clcdlyreflecting thc Lwo night modes "climb' and "straight nighl"[the laue. will bc Lermcd "sink' f.on now on for reasons ofbreviry). Obviously conditions in this conpetition were such
that pilols essentially obcyed the basic idcas underlying speedto fly thcory and thrt aligned lilt played only a minor.olc;npilots'decistuns. Undcr di erenl conditions which t-avor Lhc
occurrcncc of aligncd litl, this bimodality is likely to bc lcss
pronouoccd or 1() vanish ar all. Vr'hile this is an intercsLing
issue to be invcstigalcd, i1 is beyond the scope of the curcnl
Climb xnd sink distribulions have difierenl intcgrntcdareas with sink domi.aiing clinrb. This is less parrdoxicalrhan it migbl rppcar at first thoughl. Filst, the inallsiscompriscs morc sink thxn climb because the prc sLart data havehccn cUnrimted lrom the analysis while finrl glidc dala havenol. So cvc.y single flighl has a ret balance in favor ofsink bythc margin ofthe staf altitude. second, thc intcgrated areaisamcasure fbr the number of data points uscd in thc analysis. andthc nu rber of dala pojnts is related io the limc spenl in climbor sink. It can qualitatively he s€en thaL thc sink distribulionpexks ar a lower speed value than thc climb dislribution.Whereas the hcights gaincd in clinb rnd lost ln s;nk musL bc
the same except lor thc missing slarl allitude. the timcs spcnt
in climb or sink arc cctuinly not. An average cljmb ralc thrt is
9rJ TFCI INICAI. SOARING
largcr than the ave.age sink rate inplics that the time spent in
sink;s largerthan rhe dme spent in clinb.Fisure 4 shows ihat rhe bimodal vertical speed
disaibutions ca' bc well described by sums of rwo Gaussian
funclions, one accounting lbr climb and the other one
accounting tbr sink. The centcrs and widths of the
distribulions lhat have bccn returned as lil parameters are listed
in Table 2- Saong climb correlates wiLh larger sink, as a
conseqlencc of large. flying speeds. Thc widths of thc
disaibutions are almosl the same lor climb and siDk
distibudons and are almosl independenl of the average clinb
Time-resolyed vertical speed distributionsTime-resolved vertical speed dislributions have been
obtained lbr all th.cc drys by binning the complete sct of data
points into time intervals of30 minutcs width. FiSure 5 shows
the rimc resolved }e.tical speed disrribution for July 16 Tirne
runs from ihe bottom to the top. In contrasl lo the integrated
vertical speed distribution, here every lrace is obtained byvertically slicing thc cumulated variognnN of Fig. 2 The
analyscs of ihe other two compelition days are not shown hcre
as they yield sirnilar .csults. The gencrxl behavior oi thc
disr.ibnLions renu;ns unchrnged. with Lhc centers ol Lhc
dislribnLions moving to larger values in Lhc middle oi thc
compclition day and ihe lasl lrrcc essentially bcingcharaclerized by rhc linal glide.
As was done for the integratdd dala, every 30 minule
interlal \ras fixed by a superposition of two Grussianlunctions describing climb and sink disrribntion. Other than
tbr thc altilude distribulions, neaningtul rcsults are obtrincdtor thc whole race, fiom start lo final glide, since pilots will tryto oplimize lheir climb rate indcpcndently of Lacdcal
considerations or competition rules. A summary of the
temporal evolution ol lhe nost probablc climb and sink speeds
rt 30 minute time rcsolulion is shown in Fig. 6. Addilb.ally.Fig. 6 contains the rvcrxge chnb and sink ral€s listed in'f.tble
Altitude distributionsTime intcgrated and time rcsolved altihdc distributions
(h) were cxtrncled fion thc flight logs xs proicctions and
slices of the cumulated barograms hC) of Fig :1, similarly toLhe vertical spccd distibution cxse in the Vcrdcal speed
Tinc-in.esrrted and time-resolved altitude distributionsFigure 7 shows three tinle-integratcd altitude distributions
for cach of the rhrce tuys unde. coDsideration: lhc clinb,lrir de disi.ihutiin. the sink altitudc distribution, and thc lolalaltitude distribution which is the suln of the fbrmcr lwo Sinkxlliiude distributions have slighlly larger areas LhaD climbaltilude distributions for lhe teasons outlined in thc Tinre-intcgnted venic{l speed djstr;buLb.s seclion. Thc maindiifcreices occur.rl small altitudcs and reflect th€ iinal glideparls of the llights. Apar fftnn that, clirnb and sink altitl]dedistributions llre essentially idcndcal implying thal alliiudealeraged lcrtical speed is uDcorrelated to alLitude lndeed,ahitude alcragcd climb and sink values arc cssentially
.I':CHNICAI, SOARING
independent of altitudc as shown in Fig. 8- Altitude ave.ngcd
veftical speeds deternrinc altitude disn;bulions and must.ol bc
conluscd with maximum valu€s which do sbow a pronounc€d
dependence on altitude. Maxinum and minilnun values havc
no clfect on altitude dislributions.All altilude distribulions are singly peaked, but Lhcir
shapes are not Gaussian- Climb altitude distributions can be
well described assuming two Gaussian distributions forthermal entcring and exiting alLitud€s, as is in dehil described
in the sub section below on 'Thermal ente.ing and exitingaltiaudes Methods'.
Figu.c 9 shows the evolution of the totai allitudedisiribution over the comp€tition day lbr July 26 with a 30minute liFe resolution. Starting at the bottom, one observes
itn increase of meitn rnd maximum rlliludes together wi$ a
slight broadening of the distributio. iD the course of the day
Thc last (top) thrcc traces indicate thc trrnsition to the finalglidc regine by the "lcak-ouf' of the iltirude dislribxlionsrow.i.ls smalle. values a11he lef|
Thermal entering and exiting altitudes - MethodsDislributions of thermal cntering and exitnrg allitudes can
be obtaincd by two substantially diflbrent methods, lifl_based
and d'ffercntial, which will be dcscribed in more delail below.
The lift brscd nethod uses dircct deteminaliolr oi thcrnalentering and exiting aldludcs rclying on the identificalion ofcircling in thermal liti. Fo. idenlitication oi a thermal the
fbllowing criteria were uscd. First, the veftical spccd w musi
be positivc: dh./di > 0. Second, ground speed musl be small:
dvdr J)/Jr 0. or ' orhin(d .n one LonJiri.n. rd),/dh,
(dy/dh)'z = 0. li thcse condilions wcrc met fbr at least tourconsecutiye dxLa points. it was assumed that the glidcr had
entered rhermal lifl. and the alLituilc of the filst data pointsatisfying all xforementioned conditions was taken 1o bc the
thermrl c.tering altitude. Similarly, thermal exiting altlludes
The diffcrential method nscs indirect determinxLion ofthernal enlcring and exitjng altitudcs relying on ihe shape
analysis of climb altitude distributions. Basically, rhcrmal
entering rnd cxiting distribtrLions are obtaired by
djfferenlirLirg the climb altitudc dislibutjon with rcspccl toaltitude. Likewise, the climb nldtude distributbn can be
obtained by inlegraling thermrl c.lering and exiting allitudedistributions.
while the liil based approxch can be appli€d in a
slraighttbrward way. the basis version of the difTerenlirlapproach outlincd below requircs making the linlowingapproxinrations. First, assume lhc clirnb rate lo be constant
within a thcrmal. Second. assumc tbat fbr the aralyzcd pcriodwhich can bc a conrplete Uigbt or any parl thereor', Lhc climbrale will be lhc sarne and conslxnL litr all lhermals encountcrcd.
Thus. irsidc all analyzed thennals the same constanL average
climb rarc ol the period undcr considemtion will be
eocouotercd, which is given by thc ccnler oflhe cotresFndingGaussian vcrtical speed distribufirn f(w).
Given thc conditions describcd above. mathematicrlly the
allitude djsLribution f1h) is givcn by lhe integral
VOL.32, NO.3 JuU S.ptenber2A0il
f(h) = J(f,. (h') f"",(h')!h'
where tl"(h.) and f",'(h) nre the distributions of cnlering and
exiting altitudcs- Then, lhese distdbutioDs can be extracted
fiom a know. in flight altitude distribution i(h) which can
easily be obtained fron the analysis of fligh1 data logs.
Determining fl"(h) and io,,,(h) only requires hking the
derivative of the in flight rllilude distribution (h).
dfrh) I (h) L(h) (2rdh
Thennal enfering and exiaing altitDdes ' ResultsBoth methods, direct, liLbxsed and indirect, dilfercntial
determination of tbermal enteing and exiting altitudes wcrcperforned for all three competition days. ln the differenlialmethod. the integrated rldtude distributions obtaincd by the
procedure in the sub secLion 'Time-integ.ated aDd time'rcsolvcd altitude disiributions' were diftbrentiated, rnd the
resulLing binodal derivative was litted by a sun of twoGaussian ftnclions representing Lhcrmal entering and exitingalljtudc distributions. Ir the d;cct method, theflnal cntcrjngand cxiling dislribuiion wcrc determined from idcntilyingLhernal lift as described in rhc sub-seclion Thennrl cnteringand exiting altitudes McLhods', and boih d;stribulions were
fi1tcd by Gaussian functions. The sum of lbe two Gaussian
lunclions lvas integrated to obuin a calculated climb rlLitudcdistribution. Results oflhis procedure are Siven in fable 3 and
in FigLrre 10.
Ii can be seen that thc igreenrent of both mctbods withcach other is excellent. Trble 3 shows that, clcarly, the direct.lift-based nethod rcsults in nuch morc precisc v ues thao the
nrdirect, dilicrcntial method relying on dilforentiating lhecli'nb altitude di(ribulion. Neleriheless. ccnLcrs ltnd widths ofthermal entering nrd exiling altitude distribulions are
reproduced within Lhc cnor margins oflhe fitling procedure.
Figure I0 nnprcssively denronstrates thc excellenlagreement of bolb mclhods with each oihcr. In the lowerpanel. rhc July 23 climb altitude dislribulion synthesized frominteS.ating lifL bnsed lhernul entetirg and cxiting xltiludes is
compared 1o thc climb altitude disiribu(ion directly obtainedlion the flight bg dnta. Here. ibe liti bascd rnalysis is used as
an indirect nrclhod ior detennining allitudc distribulions. lnthe top panel ol Fig. l0 the complementxr] inibrmalion is
shown. 'fhcrmal enlering and cxitirg nltilude distribulionsdircclly obtained with the lift bascd appronch are comparcil loth€ corrcsponding distdbutions indircclly oblained wiLh thc
ditfe.cnlirl ltpproach. In this casc. the difierentjal meLhod islhe indircct one. In both cascs thc agreenrent is exccllcnt.Simila.ly, excellenl agreemcnt is also obtained lor July l6 xnd
July 26.This excellent agrecmcnl shows that lhe rssumplions of
connant vertical sFcds witbin and between Lhcrmrls were
lullilled fbr all thrcc compctition days under annlysis. Thus.Lhe agreenrent provcs Lhrt nll three days can bc vttislaclorily
VOL. 32, NO. J -.tuLt Sertenber200u
(1)dcscribed by speed to fly Lhcory. Therefbre, thc Liissecompclilion sbould be regardcd as a benchmark fbr thc case ofa pure speed-to-fly competilion, i.c. a conpetition throrghoutwhich speed-to fly thcory was applicable. Conditionsdiffering liom speed 10 ny theory conditions should easily be
recognized fron less good agreement or cven completedisagreenent of the l;ft bascd and the differential methods lbrthc delermination of the.mal entering and exiting altitude
The most relevant lactors contribuiing to such deviationsarc expecred to be l) the exislcnce of aligned lifL and 2) a w(h)correlation between (ave.aee) vertical speed and altitude.Aligned lift is noi accounlcd for in direc! dele.mination ofdrcrmnl enlering and exiting rlLiludes, whereas in thc indirectmethod iL is dealt with as if il wcrc a thermal with avcrage
climb vcrtical speed. A ion vanishing w(h) coffelalion couldbe accounlcd for in pdnciple by introducing altitude dcpcndant
weig|t laclors to fj" and f:,, distributions in equations (l) and(2). Such dcviations are expected to occur for compctilionllights in structured terain. The inlcstigation of strucluredteffain compelitions is in progrcss, and results wiu be
published in a tbrthcoming pa['er.In Tablc 4, lhe time dependeDcc of the.mal entcring
altitudes h,,,lhcrmal exiting altitudes ho,,,, nnd their dist.ibulionwidths are compired to the rnaximum .tllitudes h,,- for July 23
and July 26. Direci. lifi based dclcrmination of thermalentcring and exitlng altitudcs wns used.
For July16. no such rnalysis was pefb.med bccause the
maximun allilude was linritcd by lcgal regulatiors ralher lhan
by metcorological or llighl tactical considerations. Likcwise, atime rc$tvcd analysis was performcd only if start or final
Slide phascs did not slro.gly rilccl fie althude dislributions(ci. Fig. 3).
One obtains rhe following results: l) The altilude band
rctually used lbr uying is rclarively na ow; it covers between
2070 and 3070 ofthe maximun iltitude. 2) Thc tbcrnnl exitingaltitude lies between 75% and 8570 of llte nraximum iltitude.3) In agreement whh the prcviors 1!r'o statemenls, lhermalcnle ng altjtudes rrngc fron 507. to 65% of the maxnnumaltilude. For identifying correlations beluecn Lhcrmal enleringand exiting altitudcs and their distribution parameters withnaximunl altitudcs or vertical speed values, more data need tobe analyzed. For Lhc lime being. the drLa presented herc
suggestthat such correlations do exist.
Conclusionsll has been demonstrated lhxt r sla1is1ic analysis ol flight
Iog drla is a valuable sonrcc ol inlbflnxtion lor pilots,forccasors, and neteorologisLs. Allhough any such analysis
ncvcr directly reflects thc mctcorological situation, bul alwaysincludes the - generally unknown - pilofs lnd sailplanesrcsponse to the meteorclogical situation. lltc huge data set
xvailible and th€ dcnsity and global avrihbilily of such daLa
make them a mosl usclil lool fbr characterizing cross'counlryllling meleorohgically as well as tactically.
Vertical specd dislribulons in unstructured landscapc arc
bimodal ^nd
can bc rvell (lesffibed by ihc sunr oflwo Caussian
functiolrs, one ceote.ed 11 positlve valucs (climb)
100 TECHNICAL SOARINC
I
.ha.alterj/inc lilr :rnd onr crnrercd ar nrgJli\e vJluiq
-i-..'.r';"i ''-l*r,r' nishr ' 'rnk' va'rrrion rhroughour rhc
hce time L qentlrllY smnll'--- or"iJ.' a '','iur'."' :rre 'inslv pLake'] anJ :enerrllv
a.rmrnerric ther cJn be uell Je\cribed b) inregrariqg r$o
ilj""i." a""u,ir"*. chJJactcri"ing rh'rm renrer;ng and
J"tiins"rtitua"". rhe variation of the altitudc distributions
i",,"J,rt" 'r," ," moi pronounceJ rhrn rhJ trriJliun ol
,.','.""r -..0 disrriburion' lh' rrrirudc brnJs u'e'l arr
.J""r' '-''." rnJ J, roLrrr lor dbour /'% ol rhc thh kne's
oi the convective boundarv iaver' Generallv' cross-countrv
ivrnr ,-'na. r rr* co"Arr;""s oi rhe I ii*. comperirion rook plJcr
i..,*i.," nos,,"a 8s',.,1rhc m1\;n,um rlrirudc' sirh lo$er
a d uDoerlimiR var)ing 'lunnts the race- - i'i," rrt"r,",l' tr"'c l.tn lre*nrea ior rhe d'rermin'rion
of therrnal enrering and exiting rltitude dist'ibutions one
,"r'"i* "" ."""v'ig ,r,. be!innrnts rn'l endinr "i crr' l'n3 in
'nl.il-,t'" '.""",r r'l"g marhcm'ricJl mJnipularion ol
;iiff;il;;; dislributions Both nethods are cquiv^renl if.ta"i"td to""a-," -flv theorv coniliions are nret lt has bcen
"n.*" trtri ,Ut *r"-,tt" ."i. for all thrue Liisse conrPetition
n,', ""J", -"r"tlt
It is th€reforc suggestcd to regard the
i;i"" .""""rr',", I' i b'nchmlrr 'Fdro-r'l) Ihe' )
:'";";;"' lrt equi'Jr' n(e or borh m 'h"J' dcmonnrJr'd
i',i;" *-t will h;lp b idenlifv relevanl devirtion trom
stmdrrJ sottd'L', ily theot) condrti"ns" n. '"r'i lr" . xr*"d '; b( rsnilrc:rnrl) d;nercnr ior '
iher
*"dili;*. * pariicular in struclrred (monntainous) terrain'
undcr conditions of aligned convection. or lbr inhomogcneous
AcknowledgmentsHclolul dr\ tr.'ions dnd rririczl reading ol rhc mznu ' r ipr
rl Oiiir"' ricrli and R rlucu Nicsnt'' J'c trarelull)
acknowtedged
Rcferencesrshannon. H.,Young, G. Yates M Fnller,M andScegd'W-'":;ti..."--"rr" ir tr'**l updran intensitv ovcr complex
r".min '.inr- cm"Ao' rtile pelictn'and a sinplc boundar)
I""*i",..i, i,la", a--ai,t ta!'/ "tf'!'uo/ot!'
tr1' 2012'
"" rnr-rgl,, {i;;;. ii . youns c.. y.',c, v . Furr.,. v .nJ s"r; tr w
- i'..".-' .r'"' *1"-' -tns rish' rimr' Jno 3ll'rudc' erarr\e
'".r'"'*-. . ir'"'irr a,n't .no. ren i v /ha
'o"d'' ln4 'nol
oD 6lr-681
' i .i o i"'.",." l- , theno' R Olols'on 8 ?n rors i' f '_ i."'1..'i." t rr,-.r' rorl " r'
q 'h
clid(r F ieh Dd' i't .rhnical Sdft1..3l , 2OU
' pp- 12 5l '
+lermrkinullse. hLtp //ww$ pfts dutemikrnJlv\e/'u". i -i lr"- c, e'rturndc n
" L Ka alo lFPrmrr\' r'nnru
qcmisLhl ,4c,ot ,iPr,10 2001
' "..,i ^ r"'u.r"*.""icnPE : r4rao nS?t'UiPva tlz
,-:11:ii;';.'X .';-"::,","",2r4r8, Motorbuch vc'ras 4th cd , reTe'
pp.146_179
Table 1
Set tasks and trumber olanrllzed ilights
Accumn;te{l tracks c shown inFig l (SAA: specd arca task)
dov^',nU",ll "t
number P ol
1607 8e 43283 l:il ililHit[_19085 l8m
l5m
415?6
3 19..1 km racing33,1.5 ktrl rac;ng
286.6 km
--r,lo n s,cA t:81.1 t. - :rs l tmt365.4 kn racing')6nlTn ing26.0'1. 87
Table 2
Re,ulrs.'f lr'ring r$o GJJ"rJn drJril'ur;o" ro rh \etrill'peJJ J'rrrbrrlron\ rl l :9 4
, H\I HM: hrll \\ idrh rr hrli mc\imum\'
HWHM. m/s HWHMsink
,lay
16.07.23.01.26.O1.
2.15L401.56
l 14
0.99r06
l,411.20l3l
Lr31.061.10
TECHNICAI, SOARINGl0l vOL.32, NO.3 Jub SePtenher200E
Table 3Intcgraled thermal entcring (fiJ and thermal cxiling (i;.J altitude distributions. A; Resuhs offilting two Gaussian distributions to the derivalive of the integrated climb alitude dislributionsIroln Fig. T, based on Eq.2. B: Results offilting two Gaussian distributions to thermal entering
and exiting altiludc distributions d;reclly dclermined fron thc flight log data hi' ind h.., are
distribution centers. Maximum altitudes h-., were taken as 99.75 percentile ofaltitudc data.
(HWHM: halfwidlh at halfmaximum; A = h",/h.* - hi"/h,,")
dav fj" rt^ f"", f;",h,", m HWHM. m h.", m HWHM, m
16.07. Al6_07. B
23.07- B26.07. A,
26.01. B
ttot'+ t) 1o0,Lt5t "0/,4o2 1-4=t6' 5O.1@a
t4r,9:r l! 45Jl 20 ' 0b' )8 550= 4 { {2.odo
o12: 4q )10' :0 Ito8r tlr t)a: tl <O.s-o
950 ]) -165 b tj4br / 288 - l0 5l oq
I184_ '0 18 r0 lb/o- |/ lo8- 15 rj.ldoiq/u rt87 b 2rJtr 8 tbli= b )40 ' oo.rq
83.1% 32-4Vo
19.47o 26.59o
14.1a/. 23.89o'73.5'/o 21.69o
a5.2lo 25.lVoA25q. 22-27o
Table 4Results ofliliing 1wo Gaussian dislributions io inlegrrlcd (bold face) and timc resolved (standard face) ihermal
enlering and cj{iting altitude distribulions directly dete.mined lion ihe flight log data hii and hor are disrribution
cenrers. Maxinum aliitudes h."" were iaken as 99.75 percentile ofalLirudc daia. (HWHM: half widlh at half
maximum;A = h",L/h.^ hr"/h.",)
d"v h-",. nr fj" fi,, 1", f",,,
b,". n HWHM. m h",,,, n HWHM, mh",,,/h-,,,
23.07.to 30 1100tr.00 11,30
11.30 12.00
12.00 12.30
12.30 lt.o013.00 l3-30
26.r7.t2.00 12.30t2.30 11.00
13.00 13.30
13.30 14.001,1.00 14.3014 30 15 00
18311531
16541169189511',]9
18091970t152t781t841199220202000
288+10l97r 8
26513126I119340l.32214!19255a1424O+ 7235!22200i 924'7!1823h.t52191111951i3
sl.g0k59.27t50.6%56j%56.8%51.1%53.6%60.30k62.11o62.210603q,,56.8"h65.2q.65.t%
950+ s 265r.6 1316! 790'7!'l l60a 8 126U. /83h10 229l.11 1321,121
l001at9 305123 1403*16l\l'7!13 233+15 1506127l0l6a12 24l,rt4 1364116969111 266!13 1331+t2
ll87i 6 281! 8 1625! 61093i12 204a15 1536i19lll2!12 22+i.15 1518,1 8
I ll4r13 218!t6 l607il5ll12!23 3t0.:26 16,19113
1317i 8 209110 1162! 91301120 266!23 16711ll
73.5Va 21.6Ea82.39o 23.19o
89.2lo 29.69a'79.3Io 22]10'79.59o 22.1%16.19o 19.6q.'73.9a/o 2031oa2-5q. 22-2%8'7.7o/o 25.39a
84.97o 22.'1!aa'7.Olo 26.'79a
a2.81o 26.010a1.27o 22.0Ioai 6q. 18.570
voL. 32, NO. 3 J L\ - Sep|.mbc r 2a08 TECHNTCAL SOAR]NG
8
6
2
0
-2
-6
-8
I6
2
0
"2
160752,2
52,O
51,8
51,6
51,4
51,2
13,0 13,5 14,0 14,5
52,2
52,0
51,8
51,6
51,4
51,2
12 0 12,5 13,0 13,s 14,0 14,5
13,0 13,5 14,0 14,5
l'igure I Accumulaled tracks ibr all 254 analvzed flights
Liisse iijrtield is narked by the open circle near the uppcr lcfi
12 14 15 16
E
t
6.9
E
6'6
17
2307
..4
[,$
15.0
6
-8
8
6
2
0
'2
-6
Fiqure 2 Accumulaled variograms ior al1254 analvzed uighrs.
.!?E
t
.9
52,0
i? 51,6!
51,4
51,2
1W\d\ mJ*- xffi WX .W
2307ii-
... .,.:;..
13
TFCHNICAL SOARING t03 VOL 32, NO. :t -.tub-'Sept.nhet2008
Ez
g3
Bz
E
i rooo
t
13 14 15
3214123vertical speed, nvs
-3 -2 "1 A 12 3verticar speed, r/s
Figure 3 Accumulxlcd barograrns tbr all 25'l rnalyzed iliShts.For July 16, thc llat top betwecn 13 a.d 15 tlTC suggcsts
maximuD altirudcs xbove 3000m which underlie lcgrlrestriclions. titr July 23 and 26, maxnnum alliiudes hnn rtcindicated hy solid lines fbr 30 minutc intcrvals, except tbr sta(and finrl glidc phases. Tinre intcrlals are nunrbered whcrc
Figure 4 Normalized vc icxl speed dislributions, inlcgrnledover whole compelition days. The solid Iinc is rhe best fi1 ofrwo Gaussiar distributions lo the data. Dashcd lines describe
clinb xnd sink distributions separately.
6 5-4-3-2-1 0
voL.32, No.3 JuLr'Se c |bu2a08 TECIINICAL SOARING
16!=------
E
.-.---l---
I
E
-2 -1 01renical speed, its
Figure 5 Time-resolvcd vedical speed distributions lbr Julv
16. The lowest trnce is the first distribution aftcr task smrl(1200 1230 UTC), the upper most trace is the lasl distribudon
bcfbre finishing (1600 - 1630 UTC) Time inter""l' h'vebc{:n
sc1 to 30 minules. Dislributions are not normalized, but refl€cl
rhe rctual number of tacing cliders in each time interval.
Figure 6 Tempornl evoluthn of the most probablc (clinrb mdsink) verljcrl speeds lbr all thrce analyzed conpetition davs
with 30 rninutcs time resolution. Day avemgcd lalucs ltre
shown as straighl lines.
a( 1ud6' m
l igrrc 7 Tolal (circlcs), climb (upward Lriangles)' rnd sink(downrvard trianglcs) altilndc distrjbulio.s La.ger amplltudes
lbr sink than fbr climb reflecl liml glidc Phases Ala liom
rhat. clinb d sink disi.ibutions are csscntiallv idcntical
TECHNICAL SOARING 105 vOL. 32, NO. 3 J\IJ SePtember2A0S
2607
Bo
Iigule 8,\llirudc dependence ofaltitude averaged (largecirclcs) and cxrrcne (smll circles) clinb and sink values.Averaged values are essentialiy uncoffelared wjth altirude.whereas extreme values peak al nedium altitudes.
Figure 9 Time'resolved aititude distributions for July 26. Thelowcsl lrace is the llrst distribuiion alGr task staf ( I 130 - 1200UTC), the upper nost trace is the last dislribution beforcfinishing (1530' 1600 UTC). Time intervals have been set to30 Ininules. Distributions are nol normalized. but reflect thercturlnumber ofracing gliders in each time inierval.
Figure l0 Uppe. panel: Thclmal cnlcring alliludc f(hi")(upwcrd trianglcs) and cxiling alriludc tO*) (dorrr*ard lianglcs)altitude distibutions directil obtamed fron lift-based approach.Columns rcprcscnt thc conbincd dala f(h,.) - I(h",,J. Solid lincs arcGaussian llts 10 individual and combrned dislributions. Opcncircles ar€ d{h)/dh values oblained fiom difiere iating integntedaltihrde distributions. Lower panel: The solid line representsalljludc distnbulions obtarned fro inlcgmling ll)c co bincdlhcnnal enlering and erilmg dislribution I(ltJ - (lt.d) Opcncircies represent the altitude distribution f(h) dnecdy obtainedfrom arulysis of flight los data.
E
vot,. 32, NO. J JUL) Sett.n )er 2008 I Oal TECHN]CAL SOARING